Having started reloading over 50 years ago, I'm finding some stuff in this thread amusing. Waaaaay back then, one was supposed to make sure your primers were fully seated at the bottom of the primer pocket. That generally puts the top of the primer below the surface of the case head. If you look carefully at most factory ammo, the primers are below the surface of the case head because they're bottomed out in the primer pocket. Hand primer tools didn't exist.
Seating primers "by feel" seems to be one of those things that bench rest shooters or others seeking to minimize variation between each and every obsessively assembled round decided was "necessary". The various manufacturers jumped right on this as it was another revenue stream. The ammo factories don't seat primers by feel and that seems to work just fine. If you seat primers on the press while-but after-expanding the case necks, you can do 2 operations at the same time.
Somewhere back in the first 25 or so posts, we had the nub of the matter: tolerance stack. Primer pockets are formed by swaging, if the tools get a tad worn, the pockets become tighter than ideal. The primer cups are formed by a punch process in a die, again if parts get worn, the cups get a bit larger. Doesn't take much to cause issues.
I hate to mention another process that started with bench rest shooters, but I've found that seating primers in once fired military rifle brass is a lot easier if you uniform the primer pocket after swaging the crimp out. Yeah, it's another tedious step in initial case prep, but it pays in the long run. If you're using small primers, the same tool does both rifle and pistol cases.